In order to get inside The Institute, you'll need to progress through the game until you have the ability to built a teleportation device at one of your settlements, with help from the faction of your choice.

Once you are inside, take the elevator down and speak with the man in charge, and after which you'll be able to move around freely. Head back to the central area, where three columns are aligned around the central artium. Look for the one with the cafeteria at its base, and head up the stairs to the fourth floor where you can find a sliding door marked for Dr. Holdren. Enter his room and go out the other side onto a balcony, where you'll find the magazine.